Nicholas Williams

me my email address
I am a Postdoctoral Research Associate at the Lancaster University working with David Pauksztello, where I have been since the beginning of September 2022.

I received my doctorate from the University of Cologne in 2022 under the supervision of Sibylle Schroll. Following that, I was a JSPS short-term postdoctoral research fellow at the University of Tokyo working with Osamu Iyama from late May to late August 2022.

My research focuses on the representation theory of finite-dimensional algebras and combinatorics. In the representation theory of finite-dimensional algebras I am particularly interested in In combinatorics, I am particularly interested in I am naturally interested in the interplay between these two areas too.

You can find a copy of my CV here (updated 28/11/22).

GitHub, ResearchGate, Google Scholar, ORCID iD iconORCID

Preprints

8/2022 Stability spaces of string and band modules, (with Sibylle Schroll, Aran Tattar, Hipolito Treffinger, and Yadira Valdivieso) arXiv.
8/2022 Triangulations of prisms and preprojective algebras of type A, (with Osamu Iyama) arXiv.
06/2021 The two higher Stasheff–Tamari orders are equal, arXiv.
12/2020 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders, arXiv.

Journal publications

To appear Quiver combinatorics and triangulations of cyclic polytopes
Algebraic Combinatorics. arXiv.
10/2022 New interpretations of the higher Stasheff–Tamari orders
Advances in Mathematics. DOI, arXiv.
9/2021 The combinatorics of tensor products of higher Auslander algebras of type A, (with Jordan McMahon)
Glasgow Mathematical Journal. DOI, arXiv.

Conference proceedings

To appear The higher Stasheff–Tamari orders in representation theory
Proceedings of the 2020 International Conference on Representations of Algebras.
2021 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders
Proceedings of the 33rd International Conference on Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire 85B (2021), Art. 6, 12. Link.

Other publications

7/2022 Microthesis: Triangulations of cyclic polytopes in representation theory
London Mathematical Society Newsletter, No. 501, 33-34. Link.
4/2022 Higher-dimensional combinatorics in representation theory
Doctoral thesis, University of Cologne. Link.

Recent talks

11/2022 The higher Stasheff–Tamari orders on triangulations of cyclic polytopes
Séminaire du LaCIM, Université du Québec à Montréal
11/2022 Cyclic polytopes and representation theory
Geometry and mathematical physics seminar, University of Birmingham
11/2022 Cyclic polytopes and representation theory
Pure mathematics seminar, Lancaster University
10/2022 Mutation in higher cluster categories
Seminar@Aarhus, Aarhus University
9/2022 A structural approach to maximal green sequences
Silting theory, algebras and representations, Charles University, Prague
7/2022 Algebraic interpretation of the higher Stasheff–Tamari orders
Representation theory and various issues on related topics, Research Institute for Mathematical Sciences, Kyoto University
7/2022 Cyclic polytopes and higher Auslander–Reiten theory III
Tokyo–Nagoya algebra seminar, University of Tokyo and Nagoya University
6/2022 Cyclic polytopes and higher Auslander–Reiten theory II
Tokyo–Nagoya algebra seminar, University of Tokyo and Nagoya University
6/2022 Mutating cluster-tilting objects in (d + 2)-angulated cluster categories
FD seminar
6/2022 Cyclic polytopes and higher Auslander–Reiten theory I
Tokyo–Nagoya algebra seminar, University of Tokyo and Nagoya University
2/2022 Equivalence of maximal green sequences
Paris algebra seminar, Institut de Mathématiques de Jussieu-Paris Rive Gauche
1/2022 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders
Formal Power Series and Algebraic Combinatorics
1/2022 An algebraic interpretation of the higher Stasheff–Tamari orders
Aachen–Bochum–Cologne Darstellungstheorie Seminar
12/2021 Cyclic polytopes and higher Auslander–Reiten theory
Tokyo–Nagoya algebra seminar
4/2021 The higher Stasheff–Tamari orders in representation theory
Paris algebra seminar, Institut de Mathématiques de Jussieu-Paris Rive Gauche
3/2021 New interpretations of the higher Stasheff–Tamari orders
Diskrete Mathematik / Geometrie Forschungsseminar, TU Berlin
3/2021 The Tamari lattice in representation theory
Junior Algebra Colloquium, University of Bristol

Translations

I have translated a couple of papers of Carathéodory from German into English. I make no claim to any of the mathematics in these papers. It is also not impossible that I have introduced errors in the process of translation.

Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen
Constantin Carathéodory
Mathematische Annalen (1907), Volume: 64, pp. 95–115.
Original, Translation
Über den Variabilitätsbereich der Fourier’schen Konstanten von positiven harmonischen Funktionen
Constantin Carathéodory
Rendiconti del Circolo Matematico di Palermo (1911), Volume: 32, pp. 193–217.
Original, Translation

Categorifications in Representation Theory

I organised this conference with Aran Tattar.
Conference poster

Other

I am sometimes asked what the painting behind me on zoom is. It is one of my uncle's paintings. You can find more of his paintings here.

Leicester mathematician takes his research to Parliament